There is proposed a cooling system for a hybrid vehicle that includes an engine, a rotary electric machine and a power transmission device configured to transmit a driving force of each of the engine and the rotary electric machine to drive wheels of the vehicle through an output portion of the power transmission device, wherein the cooling system includes a first pump that is to be mechanically driven by rotation of the output portion and a second pump that is to be mechanically driven by rotation of the engine. In the proposed cooling system, when being driven, each of the first and second pumps ejects lubricant that is supplied to the rotary electric machine, for thereby cooling the rotary electric machine. For restraining increase of temperature of the rotary electric machine, an amount of the lubricant supplied to the rotary electric machine needs to be increased, particularly, where there is a need to widen a range of a vehicle running speed in which the vehicle is caused to run by the rotary electric machine with the engine being stopped. A cooling system, which is disclosed in JP2012-106599A, is an example of this type of the cooling system. In the cooling system disclosed in this document, the rotary electric machine is cooled such that an amount of the lubricant supplied from the first pump to the rotary electric machine, which is mechanically driven by rotation of the output portion of the power transmission device corresponding to the vehicle running speed, is increased with increase of the vehicle running speed, namely, with increase of an amount of heat generation by the rotary element machine.